Absence of bound states for waveguides in 2D periodic structures
Abstract
We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a perturbation in form of a line defect. The defect is aligned along one of the coordinate axes, periodic in that direction (with the same periodicity as the background), and bounded in the other direction. This setting models a so-called "soft-wall" waveguide problem. We show that there are no bound states, i.e., the spectrum of the operator under study contains no point spectrum.
Cite
@article{arxiv.1111.4578,
title = {Absence of bound states for waveguides in 2D periodic structures},
author = {Vu Hoang and Maria Radosz},
journal= {arXiv preprint arXiv:1111.4578},
year = {2015}
}
Comments
This is an updated version of our paper (in slightly different form in Journal of Mathematical Physics). An anonymous reviewer kindly made us aware that ref. 10 is not applicable in our situation. An application of the theorem in ref. 10 would have proved the absence of singular continuous spectrum also. Our result on the absence of point spectrum is not affected by this